Séminaire Lotharingien de Combinatoire, B75f (2016), 12 pp.

Xin Fang and Ghislain Fourier

Torus Fixed Points in Schubert Varieties and Normalized Median Genocchi Numbers

Abstract. We give a new proof for the fact that the number of torus fixed points for the degenerate flag variety is equal to the normalized median Genocchi number, using the identification with a certain Schubert variety. We further study the torus fixed points for the symplectic degenerate flag variety and develop a combinatorial model, symplectic Dellac configurations, to parametrize them. The number of these symplectic fixed points is conjectured to be a median Euler number.

Received: January 1, 2016. Revised: May 25, 2016. Accepted: May 25, 2016.

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